Our two-part “Math by Touch” blog series is designed to be used by teachers with their students to incorporate learning Braille with math. You’ll find creative scenarios to get students engaged, historical details, and fun puzzles. Read Part 1 here.
Computing in Braille
Just like Louis Braille, who developed the initial alphanumeric coding out of a need to communicate, math scholar Abraham Nemeth realized while at college in 1952 that he was unable to write equations and formulas using traditional Braille, which, mathematically, has only the capacity for basic numeric statements. Nemeth couldn’t use traditional Braille to express equations with both variables and coefficients (algebraic expressions like 4x - 7), but he was also limited in his ability to show exponential expressions (such as x3).
At a college level, Louis Braille’s alphabet was not strong enough to support advanced mathematical reasoning. Nemeth was discouraged by his undergraduate professors when he indicated an interest in studying math, in part due to the limitations of Braille for the subject. Ultimately, he defied the beliefs of those professors and went on to receive a Ph.D. in mathematics with the help of his innovative coding.
Today, Nemeth Braille is used primarily in math classes, and there are some distinct differences in its notation compared to the Braille alphabet developed in the 19th century.
First, students must code that they are using numeric characters by putting a single number sign in front of their written expression:
Secondly, Nemeth Braille numbers are “dropped” in their cell, meaning they are shifted down a row compared to traditional Braille number characters. Shifted down, the numbers look like this:
After the number sign has been placed, Nemeth Braille writers can transcribe any combination of characters to create multidigit numbers.
See if you can read the multi-digit numbers below:
Puzzles 1–3: Read the Number
Think you got all three? Check your work here.
Puzzle 4: Addition
Nemeth Braille gives its users the ability to write complex expressions and equations and has codes for symbols that traditional Braille does not. For example, addition, subtraction, multiplication, and division equations use the following symbols:
You may notice that the plus and minus signs only span a single Braille cell, like the letters and numbers we are now familiar with. However, the multiplication, division, and equal signs span multiple cells. Thus, when reading equations in Braille, it’s important to pay attention to spacing. See if you can read the addition problem below:
Think you got it? Check your work here.
Puzzle 5: Multiplication
Multiplication problems look similar, but require the writer to be mindful of spacing. See if you can read the multiplication problem below:
I’m sure you got this one—you’re an expert now! Check your work here.
Puzzle 6: Operation Box
Now that you’re familiar with Nemeth Braille notation, put what you know to the test with three of our “Operation Box” puzzles. The puzzles start easy and progress to more challenging. Do them in any order and reference the Nemeth Braille coding in this post as often as you need!
Check your work for all of the puzzles in this series with our answer key.
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